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A117574 Total number of permutations p of [n] such that |p(i+3) - p(i)| is not equal to 3 for 1 <= i <= n-3. 9
1, 1, 2, 6, 20, 80, 384, 2240, 15424, 123456, 1110928, 11287232, 127016304, 1565107248, 20935873872, 301974271248, 4669727780624, 77046043259824, 1350585114106416, 25062108668100208, 490725684463001488, 10109820295907492304 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
a(n) is also number of ways to place n nonattacking pieces rook + leaper[3,3] on an n X n chessboard.
LINKS
Vaclav Kotesovec, Non-attacking chess pieces, Sixth edition, p. 633, Feb 02 2013.
Roberto Tauraso, The Dinner Table Problem: The Rectangular Case, INTEGERS: Electronic Journal of Combinatorial Number Theory, Vol. 6 (2006), #A11.
FORMULA
Formula given in Tauraso reference.
Asymptotic (R. Tauraso 2006, quadratic term V. Kotesovec 2011): a(n)/n! ~ (1 + 8/n + 30/n^2)/e^2.
CROSSREFS
Column k=3 of A333706.
Sequence in context: A245373 A204440 A189839 * A177481 A177475 A118476
KEYWORD
nonn,hard
AUTHOR
James A. Sellers, Apr 27 2006
EXTENSIONS
Terms a(17)-a(28) from Vaclav Kotesovec, Apr 19 2011
Terms a(29)-a(30) from Vaclav Kotesovec, Apr 20 2012
a(0)=1 prepended by Alois P. Heinz, Feb 05 2023
STATUS
approved

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Last modified May 19 19:45 EDT 2024. Contains 372703 sequences. (Running on oeis4.)